Solve the problem.
-$x ( x + 5 ) \geq - 6$
A) $[ - 3 , - 2 ]$
B) $[ - 2 , \infty )$
C) $( - \infty , - 3 ]$
D) $( - \infty , - 3 ]$ or $[ - 2 , \infty )$

Question

Quizplus · Accepted Answer

To solve the inequality $x(x + 5) \geq -6$, we first bring all terms to one side to get a quadratic inequality: $x^2 + 5x + 6 \geq 0$. Factoring the quadratic gives $(x + 2)(x + 3) \geq 0$. The critical points are $x = -3$ and $x = -2$. Testing intervals around these points, we find that the inequality holds for $x \leq -3$ and $x \geq -2$, hence the solution is $(-\infty, -3]$ or $[-2, \infty)$.

Solve the Problem x(x+5)≥−6x ( x + 5 ) \geq - 6x(x+5)≥−6

Solve the Problem $x ( x + 5 ) \geq - 6$